SOLUTION: if a certain two digit number is divided by the sum of its digits, the quotient is 3. if the digits are reversed, the new number is 9 less then three times the original number. fin

Question 226573: if a certain two digit number is divided by the sum of its digits, the quotient is 3. if the digits are reversed, the new number is 9 less then three times the original number. find the original number.
I think i have one of the equations: I used Z as my new number and X as the original number. Z=3X-9
could you help me solve this using a set of system of equations?
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = original number and y = reversed number

Any two digit number is of the form . Ex: 21=10*2+1 (think of t is the tens digit and u as the units/ones digit)

So and (just swap t and u)

The statement "if a certain two digit number is divided by the sum of its digits, the quotient is 3" translates to (because t+u is the sum of the digits). Plug in to get . So this is our first equation.

"if the digits are reversed, the new number is 9 less then three times the original number" translates to . Plug in and to get . This is the second equation.

So you now have the system

Because you have two equations with two unknowns, you can find the unique solution which means you can find t and u. I'll let you do that. Let me know if you still need help.
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